As others have noted - you can use any fabric you wish to stitch this. This is moderately large so a fairly big piece of fabric is required, since you will probably want to frame it and that requires more than the design.
On my monitor, this looks like it's stitched on an over-dyed linen or evenweave/Lugana, not "natural' linen (YMMV). Perhaps get all the supplies and chart, then select a fabric - this is going to take some time and expense, so be sure it looks beautiful to you! Your personal taste, your budget, your time :-)